Denoising of Hyperspectral Images Employing Two-Phase Matrix Decomposition

Noise reduction is a significant preprocessing step for hyperspectral image (HSI) analysis. There are various noise sources, leading to the difficulty in developing a somewhat universal technique for noise reduction. A majority of the existing denoising strategies are designed to tackle a certain kind of noise, with somewhat idealized hypotheses imposed on them. Therefore, it is desirable to develop a noise reduction technique with high universality for various noise patterns. Matrix decomposition can decompose a given matrix into two components if they have low-rank and sparse properties. This fits the case of HSI denoising when an HSI is reorganized as a matrix, because the noise-free signal of HSI has low rank due to the high correlations within its content, while the noise of HSI has structured sparsity with respect to the big volume of data. Moreover, matrix decomposition avoids denoising process falling into the dependence on distribution characteristics of the noise or making some idealized assumptions on HSI signal and noise. In this paper, a two-phase matrix decomposition scheme is presented. First, by employing the low-rank property of HSI signal and the structured sparsity of HSI noise, the hyperspectral data matrix is decomposed into a basic signal component and a rough noise component. Then, the latter is further decomposed into a spatial compensation part and a final noise part, via using the band-by-band total variation (TV) regularization. A number of simulated and real data experiments demonstrate that the proposed approach produces superior denoising results for different HSI noise patterns within a wide range of noise levels.